⚛️ quantum physics

Charge acceleration without radiation

This paper demonstrates that, contrary to classical expectations, quantum mechanics allows electric charges to accelerate without emitting electromagnetic radiation by utilizing the Aharonov-Bohm effect, a discovery that necessitates a fundamental reconsideration of the nature of radiation.

Original authors: Yakir Aharonov, Daniel Collins, Sandu Popescu

Published 2026-02-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yakir Aharonov, Daniel Collins, Sandu Popescu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: Breaking the Golden Rule

For over a hundred years, physics has relied on a golden rule: If you push an electric charge (like an electron) to make it speed up or slow down, it must scream.

That "scream" is electromagnetic radiation (light, radio waves, X-rays). It's the same reason your phone gets hot when you use it, or why a radio antenna needs to wiggle electrons to send a signal. The rule is: Acceleration = Radiation.

This paper says: "Not in the quantum world."

The authors, led by the famous physicist Yakir Aharonov, have proven that you can accelerate an electron without it screaming a single bit of radiation. They did this by using a "quantum loophole" that doesn't exist in our everyday, classical world.

The Analogy: The Ghostly Train and the Invisible Wall

To understand how this works, imagine a very strange train (the electron) that can be in two places at once.

1. The Setup: The Split Train

Imagine our electron isn't just one solid ball; it's a "wave" that has split into two separate train cars, Car A and Car B.

Car A is on the left side of a track.
Car B is on the right side of the track.
They are far apart, so they can't bump into each other.

Between them, in the middle of the track, sits a Magnetic Solenoid (a coil of wire). Think of this solenoid as a "Ghost Wall."

Crucial Point: The magnetic field is trapped inside the solenoid. Outside the solenoid, where the train cars are, there is zero magnetic field. It's completely empty space.

2. The Classical Expectation

If this were a normal train, and you wanted to speed it up, you would need to push it with a force (like an engine). But here, the "Ghost Wall" exerts no force on the train cars because they never touch it.

Classical Physics: No force = No acceleration. The train keeps coasting.
Old Quantum Physics: Even if you use magic, if you accelerate a charge, it must radiate energy.

3. The Quantum Trick: The "Ghostly" Push

Here is where the magic happens. In quantum mechanics, particles are sensitive to things they can't even touch. This is called the Aharonov-Bohm effect.

Even though the train cars never touch the magnetic field, the existence of the field inside the Ghost Wall changes the "rhythm" (or phase) of the train cars.

Car A (on the left) passes by and feels nothing. Its rhythm stays the same.
Car B (on the right) passes by the other side. Even though it feels no force, the magnetic field inside the wall changes its rhythm slightly.

Now, the two cars have a mismatched rhythm. They are out of sync.

4. The Result: Acceleration Without Radiation

When you bring these two cars back together to see where the train is, their mismatched rhythms cause them to interfere with each other.

Because of this interference, the train suddenly appears to be moving faster (or slower) than before.
The Miracle: The train changed its speed (accelerated), but it never emitted a single photon of light or radio wave.

Why? Because the train never felt a physical "push." It didn't get hit by a force. It just got a "quantum nudge" from a distance. Since no force was applied locally, no energy was lost to radiation.

The "Iceberg" Metaphor

The authors say this discovery is just the "tip of the iceberg."

The Tip (What we see): We see an electron speed up without making noise.
The Iceberg (The deep truth): This changes how we understand the universe. It suggests that "acceleration" and "radiation" are not as tightly linked as we thought. In the quantum world, you can change a particle's motion using "invisible" connections (potentials) that don't require physical contact.

A Simpler Analogy: The Orchestra

Imagine an orchestra (the electron) playing a note.

Classical Rule: If the conductor waves the baton hard (acceleration), the musicians must make a loud noise (radiation).
The Paper's Discovery: The conductor can change the sheet music (the phase) for the musicians sitting on the left side of the stage, while the musicians on the right side keep their music the same.
When the musicians look at each other, the song sounds different—it sounds like the tempo has changed (acceleration).
But because the conductor never actually hit the musicians with the baton, the orchestra didn't make a single extra sound. The change happened purely in the relationship between the musicians, not in the force applied to them.

Why Does This Matter?

It breaks the "Common Sense" of Physics: We are used to thinking that to move something, you must push it, and pushing it makes noise. This paper shows that in the quantum realm, you can move things "silently" using invisible connections.
New Technology: If we can accelerate particles without them losing energy as radiation, we might be able to build much more efficient particle accelerators or quantum computers that don't overheat.
Universal Application: The authors suggest this might apply to all types of radiation, not just light. It implies our fundamental understanding of how the universe works needs a major update.

Summary

The paper proves that you can speed up an electron without it radiating energy, provided you use the weird, non-local rules of quantum mechanics (specifically the Aharonov-Bohm effect). It's like pushing a car by changing the color of the road it's driving on, rather than touching the car itself. The car speeds up, but the engine stays silent.

1. Problem Statement

The paper challenges a fundamental tenet of classical electrodynamics and the standard interpretation of Quantum Electrodynamics (QED): that any accelerated electric charge must emit electromagnetic radiation.

Classical View: Radiation is inextricably linked to acceleration caused by forces ($F=ma$).
Quantum Context: While QED generally presumes this rule holds, the authors argue that the quantum definition of acceleration differs from the classical one. In quantum mechanics, acceleration can occur without forces acting on the particle (via the Aharonov-Bohm effect), raising the question: Does a quantum particle accelerated without force still radiate?

2. Methodology

The authors propose a theoretical thought experiment utilizing dynamical non-locality and the Aharonov-Bohm (AB) effect to accelerate a charged particle without applying a local force.

The Setup

Initial State: An electron is prepared in a spatial superposition of two (or more) separated wavepackets, $\Psi_L$ and $\Psi_R$ , located on opposite sides of a region containing a magnetic flux (e.g., an infinite solenoid) or a capacitor.
The Interaction:
- The electron wavepackets pass the solenoid (or capacitor) without entering the region where the electromagnetic fields ( $E$ or $B$ ) are non-zero.
- The solenoid contains a magnetic flux $\Phi$ . The vector potential $\mathbf{A}$ is non-zero in the region where the electron travels, even though the magnetic field $\mathbf{B}$ is zero there.
Phase Accumulation:
- The wavepacket passing through the region with non-zero vector potential accumulates a phase shift relative to the other.
- For a charge $q$ , the relative phase is $\alpha = q\Phi$ (in units where $\hbar=1$ ).
- Alternatively, a time-dependent electric potential difference between two Faraday cages can induce a similar relative phase.
Acceleration Mechanism:
- The relative phase $\alpha$ modifies the interference pattern of the superposition.
- This changes the momentum probability distribution $P(p_x)$ of the electron.
- Specifically, the peak of the momentum distribution shifts from $p \approx 0$ to a target momentum $p_0$ .
- Since the momentum distribution changes, the particle is technically "accelerated."

The "No-Radiation" Argument

The authors argue that radiation is absent based on the following logic:

Linearity: The time evolution of each individual wavepacket ( $\Psi_L$ and $\Psi_R$ ) is identical to the case where the solenoid is absent (since they never experience a force). A free particle does not radiate.
Superposition: The total state is a linear superposition. Since neither component radiates, and the Coulomb fields of the components decay as $1/R^2$ (while radiation decays as $1/R$ ), the interference of the Coulomb fields cannot generate a $1/R$ radiation term.
Free Evolution: After the phase is accumulated, the particle evolves freely. Free particles do not radiate.

3. Key Contributions

Demonstration of Radiation-Free Acceleration: The paper provides a rigorous proof that a charged particle can undergo a change in momentum (acceleration) without emitting electromagnetic radiation, provided the acceleration is driven by non-local quantum effects (phase shifts) rather than local forces.
Distinction Between Local and Non-Local Effects: The authors clarify that interactions have two aspects:
- Local: Occurs where the field is present; involves forces, changes the average momentum, and produces radiation.
- Non-Local: Occurs where the field is absent but potentials exist; changes the distribution of momentum (modular variables) without changing the average momentum and without radiation.
Reinterpretation of Acceleration: The work highlights that in quantum mechanics, "acceleration" (change in momentum distribution) does not necessarily imply the presence of a force or the emission of radiation.

4. Results

The authors present specific mathematical models and limits to support their claims:

Two-Wavepacket Case:
- Initial state: Superposition of two top-hat wavepackets.
- Final state: Same superposition with a relative phase $\alpha$ .
- Result: The momentum distribution shifts from a peak at $p=0$ to a peak at $p \approx \alpha/D$ (where $D$ is the separation). The electron is accelerated, yet no radiation is emitted.
Multi-Wavepacket Limit (Arbitrary Acceleration):
- By using an array of $N$ wavepackets separated by gaps and an array of solenoids, the authors show that the electron can be accelerated from $p=0$ to an arbitrary momentum $p_0$ with probability approaching 1.
- In the limit where the gap fraction $\xi \to 0$ and the number of packets $N \to \infty$ , the final state approximates a boosted top-hat function $e^{ip_0 x}\Theta(x)$ .
Paradox of Moments:
- A counter-intuitive result is that while the momentum distribution shifts drastically (peaking at $p_0$ ), the moments of the momentum distribution (e.g., $\langle p \rangle, \langle p^2 \rangle$ ) remain unchanged compared to the initial state.
- The change in the distribution is driven by "modular variables" (non-local observables), while the standard moments are preserved because the phase shift does not alter the local probability density in a way that changes the integral of $p^n$ .

5. Significance

Foundational Physics: The paper suggests that the classical intuition linking acceleration to radiation is incomplete in the quantum regime. It forces a reconsideration of the fundamental mechanisms of radiation.
Universality: The authors argue this effect is not limited to electromagnetism but applies to any type of radiation, implying a broader principle of non-local dynamics in quantum field theory.
Technological Implications: While currently a theoretical construct, understanding radiation-free acceleration could have profound implications for quantum control, particle manipulation, and the design of future quantum technologies where energy loss via radiation is a limiting factor.
Conceptual Shift: It reinforces the concept of dynamical non-locality, demonstrating that potentials (not just fields) are the primary drivers of quantum dynamics, capable of altering particle states without local interaction.

Conclusion

The paper concludes that the standard view of radiation must be updated. In quantum mechanics, acceleration is a change in the momentum probability distribution, which can be induced non-locally via the Aharonov-Bohm effect. This process alters the particle's state without local forces and, crucially, without the emission of electromagnetic radiation, challenging the universality of the "accelerated charge radiates" dogma.